Since ancient times, the pomegranate has symbolized luck, fertility, abundance, life, and rebirth thus it is frequently encountered in ancient Greek cult and art.

Glass flask in the form of a pomegranate. Late Cypriot (1340BC-1200BC). Enkomi. British Museum. https://www.britishmuseum.org/collection/object/G_1897-0401-1052
There is an interesting article about the origin of the pomegranate vase. If you would like to read it, follow the link https://www.ascsa.edu.gr/uploads/media/hesperia/148339.pdf